Solve for $x$ : $4x^2 - 16x - 240 = 0$
Solution: Dividing both sides by $4$ gives: $ x^2 {-4}x {-60} = 0 $ The coefficient on the $x$ term is $-4$ and the constant term is $-60$ , so we need to find two numbers that add up to $-4$ and multiply to $-60$ The two numbers $6$ and $-10$ satisfy both conditions: $ {6} + {-10} = {-4} $ $ {6} \times {-10} = {-60} $ $(x + {6}) (x {-10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 6) (x -10) = 0$ $x + 6 = 0$ or $x - 10 = 0$ Thus, $x = -6$ and $x = 10$ are the solutions.